With the advent of deep sub-wavelength lithography, the relationship between width, spacing, and yield is more complex than it used to be. The conventional solution is obtained by running optical and etching simulation software to find the process window, and then simulating process variations to find the expected yield. This may be acceptable for defining process characteristics, but far too slow for a router that must make millions of width and spacing decisions to complete a single design.
In order to fabricate successfully, all lines and all spaces must print correctly. The spaces must print correctly, or else a short may occur. The lines must print correctly or an open may occur. Failure of the chip fabrication can occur for varied reasons. Three of the reasons are discussed below. First, the dose or focus might be off enough so that the line or space does not print properly. This may be referred to as an ‘optical’ problem, or a lithography problem. Second, a stray particle can land on the mask or wafer, perhaps breaking a line or causing a short. This can be referred to as a ‘particle’ problem. Third, a via can fail to work correctly, due to variety of reasons. This may be referred to as a ‘via’ problem. These challenges are described in more detail in the following paragraphs.
The particle problem is well understood. Particle size distribution can be measured for a given set of fabrication constraints. For example, FIG. 1 is a representation of a particle size distribution graph to determine the number of particles of a particular size that may be available to cause a failure. The graph shows that as the particle size decreases the number of particles in a square centimeter increases. Thus the odds of failure are reduced if the width or spacing is greater than the smaller particle sizes. However, in the absence of detailed data some particle size distribution can be assumed (1/x3 is typical).
A ‘critical area’ can be measured for any size particle—this critical area is the area of the portion of the layout where the chip would malfunction if the center of a particle of the specified size landed in this area. The particle size distribution and critical area determine the yield from this effect. In general, the details of this model have not mattered much to routers since the curve is so steep that the solution to date has been to evenly distribute any remaining space.
The optical, or lithography, problem in which the dose (i.e., exposure) and focus may be skewed, is where the recent complexities occur. Here a bigger spacing is not always better, and may be considerably worse. In fact some dimensions, even though larger than the minimum, may not be permitted at all. These “not-permitted” dimensions may be referred to as “forbidden pitches,” and result from the sophisticated optical tricks needed to print these sizes at all. For example, lithography may be optimized to print the narrowest lines and spaces. Larger spaces will then work less well, until the spacing is large enough to allow assist features (may be referred as scattering bars) to be inserted. In some cases the process window at the intermediate spacing is so small there is virtually no chance of both the space and the lines printing correctly, this is a forbidden pitch.
One prior solution is referred to as ‘design rules’. These rules may be very simple and binary in nature. Any solution that meets the rules is acceptable (and all solutions are equally acceptable), and any solutions that does not meet the rules is forbidden (and all such solutions are equally forbidden). The rules are simple, consisting of, at most, a list of spacings according to wire width, and often just a single minimum width and spacing. For example, a common routing design rule is to route a wire no closer to an object than some specified minimum spacing (typically roughly equal to the width of the wire) so that they will have enough space to function properly.
Another prior solution is referred to as ‘scripts’. Scripts are command sequences that tell the router what to do. For example, the scripts may instruct the router to first double all vias wherever there is enough space, and then route the remaining wires. These scripts are intended by the user to result in designs with increased yield. However, this is not always the case.
The drawback to both previous solutions is that they do not describe the real manufacturing system very well. In practice, different spacings and widths have different degrees of manufacturability. Second, because of the binary nature of the rules, there is no guidance once the rules are met. That is, each scenario that meets rules is treated equal to the other scenarios that meet the rules, when that may not be the case. Exact minimum spacing, twice this spacing, and so on, are all exactly as good to the router. So the router has no reason to pick one configuration over another.
Some more specific example problems include:
Existing routers cannot include considerations of lithography, particle yield, and via problems simultaneously.
Existing routers cannot make an intelligent choice among many alternatives, since all are exactly equal under the older concept of design rules.
Existing routers cannot obey the idea of ‘forbidden pitch’, where certain spacings are not permitted even though a smaller spacing is acceptable or fits within the design rules.
Existing routers cannot make an intelligent tradeoff between extra vias and increased critical area, so it must follow simple strategies such as doubling all vias, then increasing spacing, even though this may not be optimum and in fact hurt the overall yield. For example, FIG. 2 illustrates single, double and triple vias. Single via 212 is surrounded by metal 210. Double vias 222 and 224 is surrounded by metal 220 and triple vias 232, 234, 236 are surrounded by metal 230. Adjacent to the via objects is object 240. When a via is doubled or tripled the probability of the via working increases, however, the critical area between the via(s) and the adjacent object increases as well. That is, as the via yield is increased, the line printing yield may decrease or the critical area may be large enough for a particle failure. For example, single via 212 has a critical area 218. However critical area 228 associated with double vias 222 and 224 is larger than critical area 218, and thus the line printing may have a lower yield due to particle problems than single via 218. Similarly, critical area 238 associated with triple vias 232, 234, and 236 is larger still and may have a lower yield than a double via or single via.
Existing routers cannot maximize yield, which is what the user really wants. Instead it simply tries to minimize area, which may or may not lead to the maximum yield design. In particular, existing routers may never consider non-minimum sized designs, even though they may have enough increased yield to more than compensate for their larger size.
Existing router and extractor estimates of parasitics and critical areas do not take into account how the real manufactured silicon will look since it is too time consuming to do so, even though this information can be calculated.